An Explicit Formula for Restricted Partition Function through Bernoulli Polynomials
Boris Y. Rubinstein
Abstract
Explicit expressions for restricted partition function W(s, dm) and its quasiperiodic components Wj(s, dm) (called Sylvester waves) for a set of positive integers dm = \d1, d2, ..., dm\ are derived. The formulas are represented in a form of a finite sum over Bernoulli polynomials of higher order with periodic coefficients.
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